Williams, previously deputy chief revenue officer, will oversee digital direct sales, client relations and partnerships in a newly-created role as executive director, advertising at Mail Metro Media.
He will work alongside Grant Woodthorpe, who continues to oversee print ad sales as executive director, investment in what is effectively a split online and print structure.
Parent company DMG Media said Rush has "decided to move on" and has left the business, after being "at the centre" of the "successful merger" of the Daily Mail and Metro ad sales teams to create the £315m-a-year Mail Metro Media business in January.
Rush joined DMG Media from media agency MEC in 2014 and became chief revenue officer in 2016.
She played a leading role in the expansion of MailOnline, helping to double its ad sales to more than £120m in four years and offsetting most of the decline in print ad revenue.
However, MailOnline’s underlying ad growth has slowed from 20% last year to 4% during this financial year, partly because indirect traffic from search and social platforms such as Google and Facebook has tumbled.
Rush also saw her responsibilities change as a result of the Mail Metro Media merger.
She is the second chief revenue officer to depart DMG Media in two years after her predecessor, Mel Scott, exited in November 2016.
Kevin Beatty, chief executive of DMG Media, said: "I would like to thank Clare for her hard work and contribution during a period of significant change in our advertising operation and wish her every success in her future endeavours."
Rush, who declined to comment, worked through two restructurings during her time at DMG Media.
She helped Scott to unite the Daily Mail’s digital and print ad sales teams in one division in 2015 and took charge of it a year later.
Then DMG Media separated digital and print again in the wake of the Mail Metro Media merger, with Rush chiefly looking after digital, Woodthorpe, previously the managing director of commercial at Metro, taking over print, and Martin Smith, executive director, direct sales, running classified ad sales.
DMG Media dismissed suggestions at the time that it amounted to a reversal of strategy because Martin Clarke, the long-serving publisher of MailOnline, had remained in charge of all online operations after the 2015 restructuring.
Williams reports to Clarke, as Rush previously did, in the Mail Metro Media set-up. Woodthorpe and Smith report to Beatty.
Williams said: "I’m really excited about my new role working with an amazing team.
"Mail Metro Media represents the most popular newsbrands in the UK, and I look forward to partnering with our advertisers in order to deliver results for them."
Williams joined DMG Media last year. He previously spent two decades in agencies, rising to be chief trading officer at Amplifi, the trading and innovation arm of Dentsu Aegis Network.
When DMG Media created Mail Metro Media, it said it would "better serve advertisers and their agencies" but industry observers also suggested the publisher wanted to cut costs and gain scale after Reach, the owner of the Daily Mirror, bought the Daily Express and Daily Star.
DMG Media has said its total revenues have dropped 4% in the first nine months of the current financial year, which ends in September.
Ad sales slipped 2%, with print down 5% and MailOnline up 4%, and circulation revenues fell 6%.
DMG Media is bracing for further significant editorial and commercial changes as Mail on Sunday editor Geordie Greig prepares to take over in the autumn from Paul Dacre as editor-in-chief of the flagship Daily Mail after 26 years.
Greig is expected to take a different approach, not least because he supported the UK staying in the European Union, in contrast to Dacre who campaigned for Brexit.
Editor's note: This story was updated to include the role of Martin Smith